This technical note describes a collection of test statistics accounting for estimation uncertainties at the within-subject level, that can be used as alternatives to the standard t statistic in one-sample random-effect analyses, i.e. when testing the mean effect of a population. We build such test statistics by estimating the across-subject distribution of the effects using maximum likelihood under a nonparametric mixed-effect model. For inference purposes, the statistics are calibrated using permutation tests to achieve exact false positive control under a symmetry assumption regarding the across-subject distribution. The new tests are implemented in a freely available toolbox for SPM called Distance.